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math.CV2025
Completely Integrable Foliations: Singular Locus, Invariant Curves and Topological Counterparts
Javier Ribón
We study codimension holomorphic foliations defined in a neighborhood of a point of a complex manifold that are completely integrable, i.e. with independent mero…
math.CV2023
Complexity of Puiseux solutions of differential and -difference equations of order and degree one
José Cano Torres, Pedro Fortuny Ayuso, Javier Ribón
We relate the complexity of both differential and -difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are c…
math.CV2023
The Poincaré problem for reducible curves
Pedro Fortuny Ayuso, Javier Ribón
We provide sharp lower bounds for the multiplicity of a local holomorphic foliation defined in a complex surface in terms of data associated to a germ of invariant curve. Then we a…